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In Fig, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC = ∠DEF.

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Best answer

Given that,

AB ‖ DE and EC ‖ EF

To prove:

∠ABC = ∠DEF

Construction:

Produce BC to X such that it intersects DE at M

Proof: Since,

AB ‖ DE and BX is the transversal

Therefore,

∠ABC = ∠DMX (Corresponding angles) (i)

Also,

BX ‖ EF and DE is transversal

Therefore,

∠DMX = ∠DEF (Corresponding angles) (ii)

From (i) and (ii), we get

∠ABC = ∠DEF

Hence, proved

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